Yes, trading is addictive, but the only difference is that its addiction is not as rampant/tough as that of gambling and others.
The reason is that a bigger money is involved in trading, unlike gambling, where you can continue to gamble a little or a big amount, or a mix of the two, without control. The money in trading always teaches people that lesson and forces them to quit it more easily.
How do you know you are addicted to trading? Just as with other addictions, you will be unproductively and uncontrollably do it.
In trading, with every trade you do you learn something which help you in creating a future strategy. It's a fact that trading comes with experience, you have to bear loses in the start. There is no guideline that tells you how to do trading effectively, one has to figure out himself that how to handle trading properly. Whereas gambling is a different thing, where you rarely win nor you learn anything for future.